Answer: 13-5/6 is 12 and 1/6
Step-by-step explanation:
Mark me as brainliest if this helps!
F(x) = x^5 - x^3 + x
f'(x) = 5x^4 - 3x^2 + 1
f(3) = (3)^5 - (3)^3 + 3 = 243 - 27 + 3 = 219
f'(3) = 5(3)^4 - 3(3)^2 + 1 = 5(81) - 3(9) + 1 = 405 - 27 + 1 = 379
Let the required equation of the tangent line be
y = mx + c; where y = 219, m = 379, x = 3
219 = 379(3) + c = 1,137
c = 219 - 1,137 = -918
Therefore, required equation is
y = 379x - 918
1 gal = 4 quarts
3 gal = 4 * 3 = 12 quarts
12 / 2 = 6 pitchers
Answer:
115
Step-by-step explanation:
20% is one fifth. If Mary has one fifth fewer than Susan, then she has 4 fifths of what Susan has. So 92 is 4 fifths of some number.
To find out what one fifth is, you can divide 92 by 4 because it is four fifths.
92/4 = 23
So one fifth of the number of blouses Susan has is 23. Now you can multiply 23 by 5 to get the total number of blouses Susan has.
23 * 5 = 115
Answer: 15.44 m
Step-by-step explanation:
We can think this as two triangle rectangles.
In both cases, the adjacent cathetus is 120m.
When the angle is 32°, the opposite cathetus will be the height of the cliff.
When the angle is 37°, the opposite cathetus will be the heigth of the cliff plus the height of the flagpole.
Then we need to compute both of them and calculate the difference.
We can use the trigonometric relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
in this case we have:
Tan(32°) = (height of the cliff)/(120m)
Tan(32°)*120m = height of the cliff = 74.98m
Now we can use the other angle to compute:
Tan(37°) = (heigth of the cliff + heigth of the flagpole)/120m
Tan(37°)*120m = heigth of the cliff + heigth of the flagpole = 90.42m
Then the height of the flagpole will be:
H = 90.42m - 74.98m = 15.44 m
